Is increasing software complexity the most likely bottleneck to the AI singularity?
What if the complexity of the problem of self-improving the software grows at a faster rate than the AGI intelligence self-improvement?

If this turns out to be the case, then the complexity would indeed be the bottleneck.
There's a formal term for this: kolmogrov complexity or &quot;k-complexity&quot;.  (The best formal definition of intelligence I've come across is Hutter &amp; Legg's, which is broken down in the article &quot;On the definition of intelligence&quot; by our own nbro.  It will shed shed some light on the formal structure of the question at hand.

Any attempt to provide values to your d &amp; l would speculative, since we're still so far from AGI. The question would be what is the effect of any given (d,l)

The subject can definitely be treated formally in a mathematical sense the and values analyzed.  (There may even been some formulae out there, although, they are likely to be more complex, per the Hutter&amp;Legg.)
Sorry I can't give you a more formal answer--it's a good question!

Notes:
Another bottleneck would be the speed of light, essentially, &quot;bits and bytes across a pipeline&quot;.  This would be a factor in both self-replication and networked processing and memory.  You can expand bandwidth/throughput, but not infinitely.
This relates to space complexity (how much volume/memory does the algorithm require?) in addition to the k-complexity, which itself is likely to be non-trivial for anything approaching AGI.
AI Threat:
From the standpoint of neoluddism, I'm skeptical that &quot;infinitely&quot; self-optimizing superintelligence is the greatest threat.  Evolution, and economic theory, suggest that the greater danger would come from not what is most expensive, complex, &amp; capable, but that which is &quot;just good enough&quot;, cheaper and more easily replicable.  This is because decision time becomes a critical factor in a competitive environment, as does replication time.
I always bring up grey goo because it only has to be good at 1 thing to eat everything else!